Trous spectraux pour certains algorithmes de Metropolis sur ℝ

Laurent Miclo; Cyril Roberto

Séminaire de probabilités de Strasbourg (2000)

  • Volume: 34, page 336-352

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Miclo, Laurent, and Roberto, Cyril. "Trous spectraux pour certains algorithmes de Metropolis sur $\mathbb {R}$." Séminaire de probabilités de Strasbourg 34 (2000): 336-352. <http://eudml.org/doc/114046>.

@article{Miclo2000,
author = {Miclo, Laurent, Roberto, Cyril},
journal = {Séminaire de probabilités de Strasbourg},
keywords = {reversible Markov kernel; Metropolis transformation; spectral gap},
language = {fre},
pages = {336-352},
publisher = {Springer - Lecture Notes in Mathematics},
title = {Trous spectraux pour certains algorithmes de Metropolis sur $\mathbb \{R\}$},
url = {http://eudml.org/doc/114046},
volume = {34},
year = {2000},
}

TY - JOUR
AU - Miclo, Laurent
AU - Roberto, Cyril
TI - Trous spectraux pour certains algorithmes de Metropolis sur $\mathbb {R}$
JO - Séminaire de probabilités de Strasbourg
PY - 2000
PB - Springer - Lecture Notes in Mathematics
VL - 34
SP - 336
EP - 352
LA - fre
KW - reversible Markov kernel; Metropolis transformation; spectral gap
UR - http://eudml.org/doc/114046
ER -

References

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  2. [2] H.J. Brascamp and E.H. Lieb. On extensions of the Brunn-Minkowski and Prékopa-Leindler theorems, including inequalities for log concave functions, and with an application to the diffusion equation. Journal of Functional Analysis, 22:366-389, 1976. Zbl0334.26009MR450480
  3. [3] Cheeger J., A lower bound for smallest eigenvalue of the Laplacian, Problems in Analysis, Symposium in honor of S. Bochner, Princeton University Press, (1970), 195-199. Zbl0212.44903MR402831
  4. [4] Fill J.A., Eigenvalue bounds on convergence to stationarity for nonreversible Markov chains, with an application to the exclusion process, The Annals of Applied Probability, (1991) 1 (1), 62-87. Zbl0726.60069MR1097464
  5. [5] Lawler G. and Sokal A., Bounds on the L2 spectrum for Markov chains and Markov processes : a generalization of Cheeger inequality, Transactions of the American Mathematical Society, (1988) 309 (2), 557-580. Zbl0716.60073MR930082
  6. [6] S.P. Meyn and R.L. Tweedie. Markov Chains and Stochastic Stability. Springer-Verlag, 1993. Zbl0925.60001MR1287609
  7. [7] Miclo L., Trous spectraux à basse température: un contre-exemple à un comportement asymptotique escompté, Séminaire de Probabilités XXXII, Lecture Notes in Mathematics1686, Springer-Verlag, (1998), 36-55. Zbl0911.60089MR1651228
  8. [8] Miclo L., Une variante de l'inégalité de Cheeger pour les chaînes de Markov finies, ESAIM: P&S, URL: http://www.emath.fr/ps/, (1998) 2, 1-21. Zbl0929.60051
  9. [9] J. Neveu. Bases mathématiques du calcul des probabilités. Masson, 1970. Zbl0203.49901MR272004
  10. [10] Rosenthal J.S., Markov chain convergence : from finite to infinite, Stochastic Process and their applications, (1996) 62, 55-72. Zbl0849.60071MR1388762
  11. [11] L. Saloff-Coste. Lectures on finite Markov chains. In P. Bernard, editor, Lectures on Probability Theory and Statistics. Ecole d'Eté de Probabilités de Saint-Flour XXVI-1996, Lecture Notes in Mathematics 1665. Springer-Verlag, Berlin, 1997. Zbl0885.60061MR1490046
  12. [12] Sinclair A., Improved bounds for mixing rates of Markov chains and multicommodity flow, Combinatories, proba. comput., (1992) 1, 351-370. Zbl0801.90039MR1211324

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